Simplify (5/x-4)/((5-4x)/5)

$\frac{\frac{5}{x} - 4}{\frac{5 - 4 x}{5}}$

Multiply the numerator by the reciprocal of the denominator.

$(\frac{5}{x} - 4) \frac{5}{5 - 4 x}$

To write $- 4$ as a fraction with a common denominator, multiply by $\frac{x}{x}$ .

$(\frac{5}{x} - 4 \cdot \frac{x}{x}) \frac{5}{5 - 4 x}$

Combine $- 4$ and $\frac{x}{x}$ .

$(\frac{5}{x} + \frac{- 4 x}{x}) \frac{5}{5 - 4 x}$

Combine the numerators over the common denominator.

$\frac{5 - 4 x}{x} \cdot \frac{5}{5 - 4 x}$

Cancel the common factor of $5 - 4 x$ .

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Cancel the common factor.

$\frac{5 - 4 x}{x} \cdot \frac{5}{5 - 4 x}$

Rewrite the expression.

$\frac{1}{x} \cdot 5$

Combine $\frac{1}{x}$ and $5$ .

$\frac{5}{x}$

Simplify (5/x-4)/((5-4x)/5)

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